by Cheung Kei Wai. / Parallel title in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 119-123). / Acknowledgement --- p.ii / Abstract --- p.iii / List of Abbreviations --- p.vii / List of Figure and Table Captions --- p.viii / List of Publication --- p.xiii / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Normal Diffusion --- p.4 / Chapter 1.2 --- Statistical Origin of Anomalous Diffusion --- p.10 / Chapter 1.3 --- Various Models of Diffusion --- p.15 / Chapter 2. --- Scaling Theory of Hopping Transport in One Dimension --- p.21 / Chapter 2.1 --- "Scaling Exponents, the Models and their Solutions" --- p.22 / Chapter 2.2 --- Numerical Simulations --- p.32 / Chapter 2.3 --- Relations to Diffusion on Fractals and Hierarchical Structures --- p.37 / Chapter 2.4 --- Non-Markovian Nature of Results and Quasi-localization Effect --- p.42 / Chapter 3. --- Renormalization Group (RG) Analysis of the Problem --- p.43 / Chapter 3.1 --- The Length Scale Renormalization (LSR) --- p.45 / Chapter 3.2 --- Application of the LSR to Random Barrier Model --- p.52 / Chapter 3.2.1 --- The distribution of the renormalized coupling constants / Chapter 3.2.2 --- Behaviour of W and V under the LSR transformation / Chapter 3.3.3 --- The scaling exponents from LSR / Chapter 3.3 --- Scaling Form of Diffusion Front --- p.66 / Chapter 4. --- Diffusion in Hierarchical Systems --- p.72 / Chapter 4.1 --- Scaling and Probability Densities --- p.75 / Chapter 4.2 --- Exact Renormalization and Lattice Green Function --- p.82 / Chapter 4.3 --- The Range of Diffusion --- p.89 / Chapter 5. --- Biased Diffusion --- p.95 / Chapter 5.1 --- Scaling Theory --- p.98 / Chapter 5.1.1 --- Linear Response / Chapter 5.1.2 --- Diffusion-Drift Crossover / Chapter 5.2 --- Crossover Behaviour under an Additional Bias --- p.103 / Chapter 6. --- Physical Realizations and Related Problems --- p.108 / Chapter 6.1 --- Physical Realizations --- p.109 / Chapter 6.2 --- Equivalence with Random Resistor Network (RRN) Problems --- p.113 / Chapter 7. --- Discussion and Conclusion --- p.116 / References --- p.119 / Chapter Appendix A --- Derivation of Eq. (1.3.8) --- p.124 / Chapter Appendix B --- Derivation of Eq. (1.3.10) --- p.126 / Chapter Appendix C --- Sampling from a Distribution --- p.129 / Chapter Appendix D --- Scaling Form of P (s) in Ordered System --- p.130 / Chapter Appendix E --- Explicit Form of the Lattice Green Function --- p.132
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_318991 |
| Date | January 1992 |
| Contributors | Cheung, Kei Wai., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xiii, 134 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
Page generated in 0.0022 seconds